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Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces. (English) Zbl 1236.65060

Summary: We show convergence of a finite difference scheme to solve the abstract Cauchy problem on a scale of Banach spaces which includes that for Kowalevskaya’s system. We show convergence of consistent difference schemes even for unstable cases.

MSC:

65J08 Numerical solutions to abstract evolution equations
65J10 Numerical solutions to equations with linear operators
47D06 One-parameter semigroups and linear evolution equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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[5] T. Yamanaka, Note on Kowalevskaja’s system of partial differential equations, Comment. Math. Univ. St. Paul 9 (1961), 7-10. · Zbl 0122.35302
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